A conventional scale is used in order to measure a dimension or a distance on a figure and on a map which are drawn in an enlarged manner or in a reduced manner, the conventional scale having its fixed contraction scale or its fixed scale. The typical conventional scale is shown in FIG. 20 as a triangular scale 41 which has a shape of triangle pole for example. The triangular scale 41 has a total of three measuring planes for measuring the distance or other measuring objects. According to the front view of the triangular scale 41, each measuring plane has a shape of substantially a rectangle which are enclosed by four sides. The respective longer two sides thereof has different graduation lines of respective reductions and enlargements. More specifically, there are six kinds of graduation lines since each rectangular measuring plane of the three measuring planes has two kinds of graduation lines. The following is one example of a set of contraction scales: 1/100, 1/200, 1/300, 1/400, 1/500, and 1/600. Hereinafter, the respective six kinds of graduation lines are referred to as a graduation lines group. Namely, for example, each of six kinds of graduation lines of 1/100, 1/200, 1/300, 1/400, 1/500, and 1/600 is referred to as a graduation line group.
When a distance on the map is measured by the use of the triangular scale 41 having the above-mentioned structure, after selecting one of the six graduation lines group which coincides with the contraction scale of the map, the triangular scale 41 is set such that the selected graduation lines group is placed in the vicinity of a target region to be measured. Thereafter, the target distance is measured based on the read out graduation lines.
By the way, an angle has been conventionally measured by the use of a protractor by directly reading out the graduation lines marked on the protractor. Alternatively, when the protractor is not available but a straight scale, which can measure a distance, and a triangular scale having a right angle (90.degree.) are available, the plotting by the use of these scales is carried out. Thereafter calculation for the angle with a portable calculator dealing with functional calculus is carried out by the use of the Pythagorean theorem and the inverse trigonometric functions (sin.sup.-1, cos.sup.-1, tan.sup.-1, and so on), thereby obtaining the target angle. These procedures for measuring the target angle require relatively many proceeding steps. In that case, a triangular scale having at least one side, on which graduation lines are marked, alone may be used instead of using the above-mentioned straight scale and triangular scale.
The following deals with the way to obtain the target angle based on the calculation by the plotting with the straight scale and triangular scale.
It is assumed that an angle made by two straight lines which are not parallel with each other should be measured. A perpendicular is plotted from a point on one of the two straight lines to the other straight line. Note that the straight line may be a line segment or may be a half line. After the plotting, as a right triangle can be made by the perpendicular and the two straight lines, the lengths of at least two sides of the right triangle is measured. The remaining one side of the right triangle can be obtained by the use of the Pythagorean theorem. And, the target angle can be calculated based on the lengths of the three sides of the right triangle by the use of the portable calculator or other device.
However, the above-mentioned triangular scale 41 has the following variety of problems.
More specifically, the contraction factor and the scale factor are restricted to for example six kinds or so according to the triangular scale 41. Accordingly, the dimension and distance on the map or on the figure, which is drawn in other contraction factor and scale factor than the above factors such as 1/150, 1/250, 1/350, 1/900, 1/1356, and 1/12937, can not be measured by the conventional triangular scale 41.
Moreover, when the conventional scale has a shape of tetragonometric, hexagonometric, heptagonometric, or octagonometric instead of trigonometric, only eight kinds, twelve kinds, fourteen kinds, sixteen kinds of graduation line groups can be respectively marked thereon. Even in the case of the triangular scale 41, it is not easy-to-use because the shape thereof is of trigonometric. Therefore, it takes more time for the measurement than an ordinary scale of flat plate. This ensures that the more kinds of graduation lines group the scale has, the worse operability the scale has. Accordingly, the scales having the shape such as tetragonometric can not be adapted to the actual measurement.
There are many kinds of units of the length such as milimeter (mm), centimeter (cm), meter (m), kilometer (km), inch (inch), feet (ft), angstrom (.ANG.), micron (.mu.m), Japanese shaku, yard (yard), and mile (mile). However, the conventional scale has about one kind of unit marked thereon. Accordingly, the conventional scales can not measure the figure and map which have arbitrary contraction factor or scale factor by the direct reading of the graduation lines of the scale. More specifically, when other unit than that marked on the scale is needed, the portable calculator or other apparatus is timely used for the unit conversion. For example, the unit conversion is carried out from 98 cm into the corresponding inch, thereby prolonging the required time for the measurement and thereby leading the conversion in error.
In case of the triangular scale 41, it is required to concentrate on the small graduation lines so as to measure the measuring object as accurate as possible, thereby causing the eyes of the operator to get fatigued. In especial, when the measurements of the length (or distance) should be carried out repeatedly, the fatigues are accumulated, thereby making the operability remarkably worse.
Moreover, it is impossible for the conventional scale to measure a curve length. The conventional scale can measure the curve length when it is assumed that the curve is comprised of a plurality of small line segments. In that case, the measuring numbers corresponding to that of the small line segments is required for measuring the curve length. In order to do so, much labor is not only required but also big errors occurred due to the accumulation of the respective measuring errors.
When a predetermined regional area is measured, it is required to carry out the conversion of the unit and the complicated calculations by the use of the portable calculator or other device. Moreover, when the regional area is drawn in reduction or enlargement manner, it takes remarkable long time for the calculations of the regional area. So, the conventional scale has the deficit that it is impossible to accurately measure a regional area when the regional area has a complicated shape.
The conventional angle measurement has the following problems.
More specifically, when the protractor is used for the angle measurement, like the triangular scale case, it is required that the operator concentrates on the small graduation lines so as to measure the measuring object as accurate as possible, thereby causing the eyes of the operator to get fatigued. In especial, when the measurements of the length (or distance) should be carried out repeatedly, the fatigues are accumulated, thereby making the operability remarkably worse.
In contrast, when the angle measurement is carried out by the use of the straight scale and triangular scale, it is required to carry out the remarkable complicated plotting until getting the calculated results. In addition thereto, it is required to directly plot with respect to a master drawing sheet wherein the two straight lines associated with the angle to be measured, thereby causing the master drawing sheet to be remarkably dirty.